Authors: Roman Sverdlov
The purpose of this paper is two-fold. First, we would like to write down algebraic expression for the wave function of general excited state of harmonic oscillator which doesn't include derivative signs (this is to be contrasted with typical physics textbook which only gets rid of derivative signs for first few excited states, while leaving derivatives in when it comes to Hermite polynomial for general n). Secondly, we would like to write similar expression for two dimensional case as well. In the process of tackling two dimensions, we will highlight the interplay between Cartesian and polar coordinates in 2D in the context of an oscillator. All of the above mentioned results have probably been derived by others but unfortunately they are not easily available. The purpose of this paper is to make it easier for both students and general public to look up said results and their derivations, should the need arise. We also attempt to illustrate different angles from which one could look at the problem and this way encourage students to think more deeply about the material.
Comments: 55 Pages. I am using THE RESULTS of this paper, without derivation, in arXiv:1309.3287. At the time of posting this other paper I tried to submit the oscillator paper to arXiv as well. It was put on hold and its still on hold, after 2 years. So I submit it to viXra
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[v1] 2015-10-29 19:43:19
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